A set of natural numbers multiples of 7 less than 100 is finite or not.

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Solution

It is a finite set. Because there are finite numbers.

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A set of natural numbers is finite or not.

A set of multiples of $5$ is finite or not.

State whether each of the following sets is a finite set or an infinite set:

(i) The set of multiples of 8.

(ii) The set of integers less than 10.

(iii) The set of whole numbers less than 12.

(iv) ${x : x = 3 n - 2, n \in W, n \leq 8}$ (v) ${x : x = 3 n - 2, n \in Z, n \leq 8}$ (vi) ${x : x = \frac{n - 2}{n + 1}, n \in W}$

{1, 2, 3, . . . .}

{1, 2, 3, . . . .99, 100}

100

99

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